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The formatted source code for this file is here.
And a raw version here.
Previous work by Youngser Park can be found here.

1 Introduction

Following from previous pages, this page will focus on filtering the data before clustering to explore if filtering improves the outcome of clustering.

2 Data

Here we read in the data and select a random half of it for exploration.

featFull <- fread("../data/synapsinR_7thA.tif.Pivots.txt.2011Features.txt",showProgress=FALSE)
locFull <- fread("../data/synapsinR_7thA.tif.Pivots.txt",showProgress=FALSE)

### Setting a seed and creating an index vector
### to select half of the data
set.seed(2^10)
half1 <- sample(dim(featFull)[1],dim(featFull)[1]/2)
half2 <- setdiff(1:dim(featFull)[1],half1)

feat <- featFull[half1,]
loc <- locFull[half1,]
dim(feat)
# [1] 559649    144
## Setting the channel names
channel <- c('Synap_1','Synap_2','VGlut1_t1','VGlut1_t2','VGlut2','Vglut3',
              'psd','glur2','nmdar1','nr2b','gad','VGAT',
              'PV','Gephyr','GABAR1','GABABR','CR1','5HT1A',
              'NOS','TH','VACht','Synapo','tubuli','DAPI')

## Setting the channel types
channel.type <- c('ex.pre','ex.pre','ex.pre','ex.pre','ex.pre','in.pre.small',
                  'ex.post','ex.post','ex.post','ex.post','in.pre','in.pre',
                  'in.pre','in.post','in.post','in.post','in.pre.small','other',
                  'ex.post','other','other','ex.post','none','none')

nchannel <- length(channel)
nfeat <- ncol(feat) / nchannel

## Createing factor variables for channel and channel type sorted properly
ffchannel <- (factor(channel.type,
    levels= c("ex.pre","ex.post","in.pre","in.post","in.pre.small","other","none")
    ))
fchannel <- as.numeric(factor(channel.type,
    levels= c("ex.pre","ex.post","in.pre","in.post","in.pre.small","other","none")
    ))
ford <- order(fchannel)


## Setting up colors for channel types
Syncol <- c("#197300","#5ed155","#660000","#cc0000","#ff9933","mediumblue","gold")
ccol <- Syncol[fchannel]

exType <- factor(c(rep("ex",11),rep("in",6),rep("other",7)),ordered=TRUE)
exCol<-exType;levels(exCol) <- c("#197300","#990000","mediumblue");
exCol <- as.character(exCol)

fname <- as.vector(sapply(channel,function(x) paste0(x,paste0("F",0:5))))
names(feat) <- fname
fcol <- rep(ccol, each=6)
mycol <- colorpanel(100, "purple", "black", "green")
mycol2 <- matlab.like(nchannel)

2.1 Data transformations

f <- lapply(1:6,function(x){seq(x,ncol(feat),by=nfeat)})
featF <- lapply(f,function(x){subset(feat,select=x)})

featF0 <- featF[[1]]
f01e3 <- 1e3*data.table(apply(X=featF0, 2, function(x){((x-min(x))/(max(x)-min(x)))}))

fs <- f01e3

### Taking log_10 on data with 0's removed
ans <- apply(featF0, 1, function(row){ any(row == 0)})

logF0 <- log10(featF0[!ans,])
slogF0 <- logF0[,lapply(.SD,scale, center=TRUE,scale=TRUE)]

We now have the following data sets:

  • featF0: The feature vector looking only at the integrated brightness features.
  • fs: The feature vector scaled between \([0,1000]\).
  • logF0: The feature vector, with 0’s removed, then \(log_{10}\) is applied.
  • slogF0: The feature vector, with 0’s removed, then \(log_{10}\), then scaled by subtracting the mean and dividing by the sample standard deviation.

3 Synapse Exploration

3.0.1 Kernel Density Estimates of the marginals

df1 <- melt(as.matrix(fs))
names(df1) <- c("ind","channel","value")
df1$type <- factor(rep(ffchannel,each=dim(fs)[1]),levels=levels(ffchannel))

lvo <- c(1:5,7:10,19,22,11:16,6,17,18,20,21,23,24)
levels(df1$channel)<-levels(df1$channel)[lvo]

ts <- 22

gg1 <- ggplot(df1, aes(x=value)) + 
    scale_color_manual(values=ccol[lvo]) +
    scale_fill_manual(values=ccol[lvo]) +
    geom_histogram(aes(y=..density..,group=channel,colour=channel),bins=100) +
    geom_density(aes(group=channel, color=channel),size=1.5) +
    facet_wrap( ~ channel, scale='free', ncol=6) +
    theme(plot.title=element_text(size=ts),
          axis.title.x=element_text(size=ts),
          axis.title.y=element_text(size=ts),
          legend.title=element_text(size=ts),
          legend.text=element_text(size=ts-2),
          axis.text=element_text(size=ts-2),
          strip.text=element_text(size=ts), 
          legend.position='none')+
    ggtitle("Kernel Density Estimates of `fs` data.")

print(gg1)
Figure 1: Kernel density estimates for each channel, on fs data.

3.1 Correlations

cmatfs <- cor(fs)
corrplot(cmatfs,method="color",tl.col=ccol[ford], tl.cex=0.8)
Figure 2: Correlation on untransformed F0 data, reordered by synapse type.

3.1.1 PCA on the Correlation Matrix

pcaf0 <- prcomp(featF0,scale=TRUE, center=TRUE)
pcafs <- prcomp(fs,scale=FALSE, center=FALSE)
elpcaf0 <- getElbows(pcaf0$sdev, plot=FALSE)
elpcafs <- getElbows(pcafs$sdev, plot=FALSE)

3.2 K-means++ for \(K=2\).

We run K-means++ for \(K=2\) on the fs data.

K1 <- c(2)  ## The set of K's.
#km1 <- kmeans(pcaf0$x[,1:elpcaf0[2]], centers=K1)
set.seed(2^13)
kp1 <- kmpp(fs, k=K1)

3.2.1 Within cluster correlations

corkp11 <- cor(fs[kp1$cluster == 1,])
corkp12 <- cor(fs[kp1$cluster == 2,])

par(mfrow=c(1,2))
corrplot(corkp11,method="color",tl.col=ccol[ford], tl.cex=0.8, main='Cluster 1')
corrplot(corkp12,method="color",tl.col=ccol[ford], tl.cex=0.8, main='Cluster 2')
Figure 3: Within cluster correlations

3.2.2 Heat maps:

## Formatting data for heatmap
aggp <- aggregate(fs,by=list(lab=kp1$cluster),FUN=mean)
aggp <- as.matrix(aggp[,-1])
rownames(aggp) <- clusterFraction(kp1)

The following are heatmaps generated from clustering via K-means++

heatmap.2(as.matrix(aggp),dendrogram='row',Colv=NA,trace="none", col=mycol,colCol=ccol[ford],cexRow=0.8, keysize=1.25,symkey=FALSE,symbreaks=FALSE,scale="none", srtCol=90,main="Heatmap of `fs` data.") 
#  [1] "#197300"    "#197300"    "#197300"    "#197300"    "#197300"   
#  [6] "#5ed155"    "#5ed155"    "#5ed155"    "#5ed155"    "#5ed155"   
# [11] "#5ed155"    "#660000"    "#660000"    "#660000"    "#cc0000"   
# [16] "#cc0000"    "#cc0000"    "#ff9933"    "#ff9933"    "mediumblue"
# [21] "mediumblue" "mediumblue" "gold"       "gold"
Figure 4: Heatmap of the cluster means vs channels. Rows and columns are rearranged according to synapse type.

Percentage of data within cluster is presented on the right side of the heatmap.

3.2.3 Clusters and Spatial Location

Using the location data and the results of K-means++ we show a 3d scatter plot colored accoding to cluster.

set.seed(2^12)
s1 <- sample(dim(loc)[1],5e4)

locs1 <- loc[s1,]
locs1$cluster <- kp1$cluster[s1]

m <- table(kp1$cluster)/length(kp1$cluster)

plot3d(locs1$V1,locs1$V2,locs1$V3,
       col=ifelse(locs1$cluster==1,'#d95f02','#6a3d9a'), #orange,purple
       alpha=0.75,
       xlab='x', 
       ylab='y', 
       zlab='z')

subid <- currentSubscene3d()
rglwidget(elementId="plot3dLocations")

3.2.4 Kernel Density Estimates of the marginals | cluster

Here we look at the kernel density estimates within each cluster to compare.

df2 <- melt(as.matrix(fs))
names(df2) <- c("ind","channel","value")
df2$cluster <- kp1$cluster
df2$type <- factor(rep(ffchannel,each=dim(fs)[1]),levels=levels(ffchannel))

gg2 <- ggplot(df2, aes(x=value)) + 
    scale_colour_manual(values=ccol) + 
    scale_x_continuous(limits=c(0,400)) +
    geom_histogram(aes(y=..density..,group=channel,colour=channel),bins=250) +
    geom_density(aes(group=channel, color=channel),size=1.5) +
    facet_grid(channel ~ cluster, scale='free') + 
    theme(strip.text.y=element_text(angle=0)) +
    guides(col=guide_legend(ncol=1))
print(gg2)
Figure 5: Kernel density estimates for each channel, on fs data given cluster from km++

3.3 GABABR

## re-formatting data for use in lattice 
d1gab <- data.table(stack(fs, select=-GABABRF0))[,.(values)]
d1gab$GABABR <- fs$GABABRF0

### Adding relationship factor variables
nd <- paste0("GABABR","~",abbreviate(channel[-which(channel=="GABABR")]))

d1gab$ind <- factor(rep(nd,each=dim(fs)[1]),ordered=TRUE,levels=nd)

names(d1gab) <- c("x","y","g")

lat1 <- xyplot(y ~ x | g, data=d1gab,
       as.table=TRUE,
       colramp=BTC,
       pch='.',
       scales = list(y = list(relation = "free"),x = list(relation = "free")),
       panel=function(x,y,...){
           panel.hexbinplot(x,y,..., type='g')
           panel.loess(x,y,col='red', lwd=2,...)
        }
       )
gg3 <- ggplot(data=d1gab,aes(x=x,y=y, group=g)) +   
        geom_point(pch='.',alpha=0.2) + 
        geom_hex(bins=100) +
        geom_smooth(method='lm',colour='red', alpha=0.7)+
        facet_wrap( ~ g, scales='free_x') 
print(gg3)
Figure 6: Pairs plots of GABABR and all other markers with regression lines.